Question

A sphere of mass 10kg is placed b/w two wedges as shown, if all surfaces are smooth; calculate
N1/N2
a)1/2
b)1/root 3
c)root 3
d)2​

Answer 1

Given :-

◉ A sphere of mass m = 10 Kg is placed b/w two wedges at an angle of 60° and 30° respectively. Also, all the surfaces are smooth.

To Find :-

◉ N₁ : N₂

Solution :-

According to Newton's third law of motion every action has an equal and opposite reaction.

Here, The force of weight is being exerted on both the wedges but we know the magnitude of a normal force when the object is placed on an inclined plane (making angle θ with the horizontal) is given by mgcosθ where,

• m = Mass of body
• g = Acceleration due to gravity
• θ = angle between between the inclined plane and the horizontal.

For N₁ , we have

⇒ N₁ = mg cos 60° ...(1)

Similarly, for N₂

⇒ N₂ = mg cos 30° ...(2)

But we have to find N₁ / N₂ , so we divided (1) by (2),

⇒ N₁ / N₂ = mg cos 60° / mg cos 30°

⇒ N₁ / N₂ = cos(90° - 30°) / cos 30°

⇒ N₁ / N₂ = sin 30° / cos 30° [ cos(90 - θ) = sin θ ]

⇒ N₁ / N₂ = tan 30° [ sin θ / cos θ = tan θ ]

⇒ N₁ / N₂ = 1/√3 [ tan 30° = 1/√3 ]

Since, N₁ : N₂ is 1 : √3

Therefore, Option B is correct.